hs10201f10

# hs10201f10 - EMSE 201 Introduction to Materials Science &...

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EMSE 201 – Introduction to Materials Science & Engineering Fall 2010 Case Western Reserve University 1 of 4 Case School of Engineering Solution to Homework #10 Explain how answers were obtained. Give appropriate units for all numerical answers. 1) (10 points) C&R problem 12.7. Use only the linear portions of Figure 12.8. For part a), in place of C&R’s eq. 12.10, use ρ ( T ) = 25°C + a ( T – 25°C) and determine the values of 25°C and a . a) Using the data in Figure 12.8, determine the values of 25°C and a for pure copper. Take the temperature T to be in degrees Celsius. b) Determine the value of A in Equation 12.11 for nickel as an impurity in copper, using the data in Figure 12.8. c) Using the results of parts a) and b), estimate the electrical resistivity of copper containing 2.50 at% Ni at 120° C. Solution (taken in part from the publisher’s solution manual; used with permission) a) Read 25°C for pure Cu directly from the graph: 1.82 × 10 –8 Ω m (1 pt) . To determine a , pick another temperature at which to read the resistivity. Keeping in mind that a value farther away from 25 °C will improve the precision of the computation, pick –150°C = 0.52 × 10 –8 Ω m. Then, rearranging the expression above to solve for a , a = (1.82 0.52) × 10 8 Ω m [ ] 25 − − 150 ( ) ° C [ ] = 7.4 × 10 11 Ω m ° C 1 (2 pts) b) Calculate A by rearranging Equation 12.11: A = i c i (1 c i ) In Figure 12.8, curves are plotted for three c i values (0.0112, 0.0216, and 0.0332). Find A for each of these compositions by taking a total from each curve at some temperature (say 25 ° C) and then subtracting out i for pure copper at this same temperature. Below are tabulated values of A determined from these three c i values, and other data that were used in the computations. c i 1 – c i 25°C ( Ω -m) ρ i ( Ω m) A ( Ω m) 0.0112 0.989 3.16 × 10 -8 1.34 × 10 -8 1.21 × 10 -6 0.0216 0.978 4.35 × 10 -8 2.53 × 10 -8 1.20 × 10 -6 0.0332 0.967 5.67 × 10 -8 3.85 × 10 -8 1.20 × 10 -6 The average of these three A values is 1.20 × 10 -6 [ Ω m] (3 pts) . c) Use the results of parts a) and b) to estimate the electrical resistivity of copper containing 2.50 at% Ni ( c i = 0.025) at 120 Ę C. Matthiesen’s rule says that the total resistivity is the sum of the thermal effect on, plus the effect of the Ni additions to, pure copper: 2.5%Ni,120°C = Cu,120°C + i,2.5%Ni

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EMSE 201 – Introduction to Materials Science & Engineering Fall 2010 Case Western Reserve University 2 of 4 Case School of Engineering Incorporating the expressions for ρ t and i from Equations 12.10 and 12.11, and the values of 25°C , a , and A determined above, leads to: total = 25°C + a T 25 ( ) + Ac i (1 c i ) = 1.82 × 10 -8 Ω m [ ] + 7.4 × 10 11 Ω m ° C 1
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## This document was uploaded on 11/08/2011.

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hs10201f10 - EMSE 201 Introduction to Materials Science &...

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